# High School Physics : Understanding Motion in One Dimension

## Example Questions

### Example Question #11 : Motion And Mechanics

A ball is thrown vertically with an initial velocity of . What is the maximum height it will reach?

Explanation:

To solve this problem, remember that when something is thrown vertically, its velocity will be  at the highest point. Using this principle, we know the initial velocity, final velocity (zero), and the acceleration. With the appropriate motion equation, we can solve for the distance traveled.

The best equation for this problem is:

Use the given values to solve for the distance.

### Example Question #12 : Motion And Mechanics

Two balls, one with mass  and one with mass , are dropped from  above the ground. Which ball hits the ground first?

The  mass hits first

The  mass hits first

We must know the forces to draw a conclusion

We must know the final velocities to draw a conclusion

They hit the ground at the same time

They hit the ground at the same time

Explanation:

The mass of an object is completely unrelated to its free-fall motion. The equation for the vertical motion for an object in freefall is:

Notice, there is no mention of mass anywhere in this equation. The only thing that affects the time an object takes to hit the ground is the acceleration due to gravity and the distance travelled. Since these objects travel the same distance and are affected by the same gravitational force, they will fall for the same amount of time and hit the ground together.

### Example Question #13 : Motion And Mechanics

Two balls, one with mass  and one with mass , are dropped from  above the ground. How long does it take the  ball to hit the ground?

Explanation:

The equation for the vertical motion for an object in freefall is:

Notice that there is no place for mass anywhere in this equation. This means that the two balls will be in the air for the same amount of time. We simply need to use the distance and acceleration to solve for the time.

Remember that even though the height is , the DISPLACEMENT will be . Displacement is a vector; since the direction of the distance is downward, the displacement will be negative.

### Example Question #14 : Motion And Mechanics

Two balls, one with mass  and one with mass , are dropped from  above the ground. How long does it take the  ball to hit the ground?

Explanation:

The equation for the vertical motion for an object in freefall is:

Notice that there is no place for mass anywhere in this equation. This means that the two balls will be in the air for the same amount of time. We simply need to use the distance and acceleration to solve for the time.

Remember that even though the height is , the DISPLACEMENT will be . Displacement is a vector; since the direction of the distance is downward, the displacement will be negative.

### Example Question #11 : Motion And Mechanics

Two balls, one with mass  and one with mass , are dropped from rest. It takes  for them to hit the ground. What is the final velocity of the  ball right before it hits the ground?

Explanation:

When dealing with simple vertical motion, the final velocity can be found from the initial velocity, acceleration, and time.

Remember that because the ball is dropped from rest, the initial velocity will be zero.

Notice that mass is not a variable in this calculation; the final velocity will be the same for any mass dropped from rest that is in the air for .

Use the values given in the question to solve for the final velocity.

Note that the velocity is negative because the object is traveling downward.

### Example Question #16 : Motion And Mechanics

Two balls, one with mass  and one with mass , are dropped from rest. It takes  for them to hit the ground. What is the final velocity of the  ball right before it hits the ground?

Explanation:

When dealing with simple vertical motion, the final velocity can be found from the initial velocity, acceleration, and time.

Remember that because the ball is dropped from rest, the initial velocity will be zero.

Notice that mass is not a variable in this calculation; the final velocity will be the same for any mass dropped from rest that is in the air for .

Use the values given in the question to solve for the final velocity.

Note that the velocity is negative because the object is traveling downward.

### Example Question #17 : Motion And Mechanics

A  crate slides along a frictionless surface. If it maintains a constant velocity of , what is the net acceleration on the crate?

Explanation:

Acceleration is the change in velocity per unit time.

Since the velocity does not change from one moment to the next, then there must be no net acceleration on the object.

### Example Question #18 : Motion And Mechanics

A crate has an initial velocity of . If it accelerates at a constant rate of  for , what is the final velocity?

Explanation:

For this problem, we use the formula .

We are given the initial velocity, acceleration, and time. Using these values, we can solve for the final velocity.

### Example Question #19 : Motion And Mechanics

A box moves at  across a frictionless surface. Assuming no other forces, how far will it travel in ?

Explanation:

The relationship between distance, velocity, and time is given by the formula for velocity:

We can rearrange this equation to solve for the distance.

Using the values given for the velocity and the time, we can find the distance traveled.

### Example Question #20 : Motion And Mechanics

A ball rolls at . Assuming no outside forces, how long will it take for the ball to roll ?